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Convergence Performance of the Simplified Set-Membership Affine Projection Algorithm

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Abstract

Set-membership (SM) adaptive filtering is appealing in many practical situations, particularly those with inherent power and computational constraints. The main feature of the SM algorithms is their data-selective coefficient update leading to lower computational complexity and power consumption. The set-membership affine projection (SM-AP) algorithm does not trade convergence speed with misadjustment and computation complexity as many existing adaptive filtering algorithms. In this work analytical results related to the SM-AP algorithm are presented for the first time, providing tools to setup its parameters as well as some interpretation to its desirable features. The analysis results in expressions for the excess mean square error (MSE) in stationary environments and the transient behavior of the learning curves. Simulation results confirm the accuracy of the analysis and the good features of the SM-AP algorithms.

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References

  1. J.A. Apolinário, M.L.R. de Campos, P.S.R. Diniz, The binormalized data-reusing LMS algorithm. IEEE Trans. Signal Process. 48, 3235–3242 (2000)

    Article  Google Scholar 

  2. J.R. Deller, Set-membership identification in digital signal processing. IEEE Trans. Acoust. Speech Signal Process. Mag. 6, 4–20 (1989)

    Google Scholar 

  3. P.S.R. Diniz, Adaptive Filtering: Algorithms and Practical Implementation, 3rd edn. (Springer, New York, 2008)

    MATH  Google Scholar 

  4. P.S.R. Diniz, S. Werner, Set-membership binormalized data reusing LMS algorithms. IEEE Trans. Signal Process. 51, 124–134 (2003)

    MathSciNet  Google Scholar 

  5. P.S.R. Diniz, R.P. Braga, S. Werner, Set-membership affine projection algorithm for echo cancellation, in Proc. IEEE Intern. Symposium on Circuits and Systems, Island of Kos, Greece, May (2006), pp. 405–408

    Google Scholar 

  6. E. Fogel, Y.-F. Huang, On the value of information in system identification—bounded noise case. Automatica 18, 229–238 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  7. J.F. Galdino, J.A. Apolinário, Jr., M.L.R. de Campos, A set-membership NLMS algorithm with time-varying error bound, in Proc. IEEE Intern. Symposium on Circuits and Systems, Island of Kos, Greece, May (2006), pp. 277–280

    Google Scholar 

  8. S.L. Gay, S. Tavathia, The fast affine projection algorithm, in Proc. IEEE Int. Conf. on Acoust., Speech, and Signal Processing, Detroit, MI, May (1995), pp. 3023–3026

    Google Scholar 

  9. S. Gollamudi, S. Nagaraj, S. Kapoor, Y.-F. Huang, Set-membership adaptive equalization and updater-shared implementation for multiple channel communications systems. IEEE Trans. Signal Process. 46, 2372–2384 (1998)

    Article  Google Scholar 

  10. S. Gollamudi, S. Nagaraj, S. Kapoor, Y.-F. Huang, Set-membership filtering and a set-membership normalized LMS algorithm with an adaptive step size. IEEE Signal Process. Lett. 5, 111–114 (1998)

    Article  Google Scholar 

  11. L. Guo, Y.-F. Huang, Set-membership adaptive filtering with parameter-dependent error bound tuning, in Proc. IEEE Intern. Conf. on Acoust. Speech and Signal Processing, Philadelphia, PA, May (2005), pp. IV-369–IV-372

    Google Scholar 

  12. T. Hinamoto, S. Mackawa, Extended theory of learning identification. Trans. IEE Jpn. 95-C, 227–234 (1975)

    Google Scholar 

  13. K. Ozeki, T. Umeda, An adaptive filtering algorithm using an orthogonal projection to an affine subspace and its properties. Electr. Commun. Jpn. 67-A, 19–27 (1984)

    MathSciNet  Google Scholar 

  14. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd edn. (McGraw Hill, New York, 1991)

    Google Scholar 

  15. R. Price, A useful theorem for nonlinear devises having Gaussian inputs. IEEE Trans. Inf. Theory IT-4, 69–72 (1958)

    Article  Google Scholar 

  16. A.H. Sayed, M. Rupp, Error-energy bounds for adaptive gradient algorithms. IEEE Trans. Signal Process. 44, 1982–1989 (1996)

    Article  Google Scholar 

  17. S.G. Sankaran, A.A. (Louis) Beex, Convergence behavior of affine projection algorithms. IEEE Trans. Signal Process. 48, 1086–1096 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  18. F.C. Schweppe, Recursive state estimate: Unknown but bounded errors and system inputs. IEEE Trans. Autom. Control 13, 22–28 (1968)

    Article  Google Scholar 

  19. H.-C. Shin, A.H. Sayed, Mean-square performance of a family of affine projection algorithms. IEEE Trans. Signal Process. 52, 90–102 (2004)

    Article  MathSciNet  Google Scholar 

  20. S. Werner, P.S.R. Diniz, Set-membership affine projection algorithm. IEEE Signal Process. Lett. 8, 231–235 (2001)

    Article  Google Scholar 

  21. S. Werner, M.L.R. de Campos, P.S.R. Diniz, Partial-update NLMS algorithm with data-selective updating. IEEE Trans. Signal Process. 52, 938–949 (2004)

    Article  MathSciNet  Google Scholar 

  22. S. Werner, P.S.R. Diniz, J.E.W. Moreira, Set-membership affine projection algorithm with variable data-reuse factor, in Proc. IEEE Intern. Symposium on Circuits and Systems, Island of Kos, Greece, May (2006), pp. 261–264

    Google Scholar 

  23. N.R. Yousef, A.H. Sayed, A unified approach to the steady-state and tracking analyses of adaptive filters. IEEE Trans. Signal Process. 49, 314–324 (2001)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. LPS – Programa de Engenharia Elétrica, COPPE/Poli/UFRJ, Cx. P. 68504, Rio de Janeiro, RJ, Brazil

    Paulo S. R. Diniz

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  1. Paulo S. R. Diniz
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Correspondence to Paulo S. R. Diniz.

Additional information

The author would like to thank the financial support provided by CNPq and FAPERJ, national and state research councils, respectively. He also wants to thank Markus V.S. Lima for carefully reading the manuscript and for checking the simulations.

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Diniz, P.S.R. Convergence Performance of the Simplified Set-Membership Affine Projection Algorithm. Circuits Syst Signal Process 30, 439–462 (2011). https://doi.org/10.1007/s00034-010-9219-z

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  • DOI: https://doi.org/10.1007/s00034-010-9219-z

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